Market Power

Besanko and Braeutigam, CH 11

Hans Martinez

Western University

Market Power

  • When an individual agent can affect the price (or other outcome) that prevails in the market, the agent has market power

  • A monopoly market consists of a single seller facing many buyers

  • A monopsony market consists of a single buyer facing many sellers

Monopoly

  • In contrast to a perfectly competitive firm, a monopolist sets the market price of its product (market power)

  • The demand curve stops the monopolist from setting an infinitely high price by imposing a trade-off

    • The higher the price, the lower the quantity it sells
    • The lower the price, the higher the quantity it sells

Monopolist’s Demand Curve

  • The monopolist’s demand curve is the market demand curve

  • The profit-maximizing monopolist’s problem is finding the optimal trade-off between volume and margin (difference between price and marginal cost)

Monopolist’s Problem

The monopolist’s profit-maximization problem : \[ \begin{aligned} \max_Q \pi(Q)&=TR(Q)-TC(Q) \\ \text{s.t. }& TR(Q)=QP(Q) \end{aligned} \qquad(1)\]

  • where \(P(Q)\) is the inverse market demand

Optimality Condition

  1. Profits are maximized at \(Q^*\) such that \(MR(Q^*)=MC(Q^*)\)

  2. Slope of the \(MC\) curve exceeds the slope of the \(MR\) curve

Optimality Condition

Elasticity

Marginal Revenue

  • \(MR(Q)=\frac{d TR(Q)}{dQ}\)
    • \(=P+Q\frac{dP(Q)}{dQ}\)
  • \(MR = \frac{\Delta TR}{\Delta Q}=\frac{P\Delta Q+Q\Delta P}{\Delta Q}\)
    • \(=P+Q\frac{\Delta P}{\Delta Q}\)

Marginal Revenue

Competitive firms is not affected by the change in price due to its change in output

Marginal Revenue

  • Marginal revenue has two parts:

    • \(P\): increase in revenue due to higher volume -the marginal units
    • \(Q(dP(Q)/dQ)\): decrease in revenue due to reduced price of the inframarginal units (negative)
  • The marginal revenue is less than the price the monopolist can charge to sell that quantity for any \(Q\ge0\) because \(dP(Q)/dQ\le0\)

  • MR can be positive or negative

Marginal Revenue

  • \(AR(Q)=TR(Q)/Q\)
    • \(=QP(Q)/Q=P(Q)\)
  • \(MR(Q) \le P(Q)\)
    • \(\implies MR(Q) \le AR(Q)\)

Profit-Maximization Condition

Suppose the monopolist faces a linear demand curve

\[ P(Q)=a-bQ \]

Then, the revenue function is

\[ TR(Q)=QP(Q)=aQ-bQ^2 \]

and the marginal revenue function is

\[ MR(Q)=a-2bQ \]

Profit-Maximization Condition

Monopoly vs Competitive Market

  • \(P_M>MC_M\), in general \(P_M > P_{PC}\)
  • \(Q^*_{M} < Q^*_{PC}\)
  • \(\pi_{M}\ge0\)
  • Consumers are worse off but the firm is better off. What’s best?

Monopoly is not Pareto Efficient

  • Pareto Efficiency: There is no way to make someone better off without making somebody else worse off

  • Inverse demand curve: At each level of output, \(P(Q)\) measures how much people are willing to pay for an additional unit of the good

Monopoly is not Pareto Efficient

  • Since \(P(Q)\ge MC(Q)\) for all output levels between \(Q_M\) and \(Q_C\)

  • There is a range of consumers that are willing to pay \(\bar P\) for an extra unit of output, such that \(P(Q)>\bar P> MC(Q)\) (area under demand curve between \(Q_M\) and \(Q_C\) and above the \(MC(Q)\))

Inefficiency of Monopoly

  • Any of these consumers would be better off because they are willing to pay \(P(Q)\) but the extra unit of output is sold at \(\bar P < P(Q)\)

  • Likewise, the firm would be better off because it cost \(MC(Q)\) to produce the extra unit of output and the firms sold it for \(\bar P > MC(Q)\)(all the other units of output are being sold for the same price \(P_M\) as before)

  • We found a Pareto improvement!

Inefficiency of Monopoly (continued)

Welfare Economics of Monopoly

  • How inefficient is a Monopoly?

  • Compare changes in producer’s and consumer’s surplus from a movement from Monopoly to Perfect Competition

  • Change in producer’s surplus —firm’s profits— measures how much the owners would be willing to pay to get the higher price under monopoly

  • Change in consumers’ surplus measures how much the consumers would have to be paid to compensate them for the higher price

Deadweight Loss of Monopoly

Deadweight Loss of Monopoly

  • Producer loses A, but gains C

  • Consumer gains A and B

  • A is just a transfer; total surplus does not change

  • B+C is a real gain in surplus

  • Deadweight Loss of Monopoly (B+C) measures how much worse off people are paying the monopoly price than paying the competitive price

  • DWL values each unit of lost output at the price that people are willing to pay for that unit

No Unique Supply Curve for Monopolists

  • In Competitive Markets, \(P=MC(Q)\), there is a unique relationship between the quantity produced by the firm and price \(Q=MC^{-1}(P)\)

  • In Monopoly, \(P+Q\frac{dP(Q)}{dQ}=MC(Q)\)

  • Depending on the shape of the demand curve,\(\frac{dP(Q)}{dQ}\), the monopolist might produce the same quantity at two different prices or produce different quantities at the same price

    • no unique relationship between \(Q\) and \(P\), \(\implies\) no unique supply curve

No Unique Supply Curve

Elasticity of Demand

\[ \begin{aligned} MR(Q)&=P+Q\frac{dP(Q)}{dQ} \\ &=P\left(1+\frac{Q}{P}\frac{dP(Q)}{dQ} \right)\\ &=P\left(1+\frac{1}{\frac{P}{Q}\frac{dQ}{dP}}\right)\\ &=P\left(1+\frac{1}{\epsilon_{Q,P}}\right) \\ &=P\left(1-\frac{1}{|\epsilon_{Q,P}|}\right) \end{aligned} \]

Last line follows because price elasticity of demand \(\epsilon_{Q,P}<0\)

Elasticity of Demand

Table 1: Elasticity of Demand
Elasticity Marginal Revenue Output and Profits
\(|\epsilon_{Q,P}|<1\) \(MR<0\) Reducing output increases revenue and reduces cost, so profits necessarily increase
\(|\epsilon_{Q,P}|\ge1\) \(MR\ge 0\) Increasing output increases revenue but cost increase, optimal output lies here
\(|\epsilon_{Q,P}|=\infty\) \(MR=P\) Competitive case

Optimality Condition Graph

Elastic Part of the Curve

  • Monopolists will never choose to operate where the demand is inelastic
  1. \(MC\ge0\), at the optimum \(MR=MC\ge0\), but \(|\epsilon_{Q,P}|<1 \implies MR <0\)

  2. Any point were \(|\epsilon_{Q,P}|<1\) cannot be a profit maximum, since the monopolist could increase profits by producing less output

Pricing Rule

Profit maximizing condition is \(MR = MC\) with \(P^*\) and \(Q^*\)

\[ \begin{aligned} 𝑀𝑅(𝑄^∗ )&=𝑀𝐶(𝑄^∗ ) \\ 𝑃^∗ \left(1-\frac{1}{|\epsilon_{𝑄,𝑃}|}\right)&=𝑀𝐶(𝑄^∗) \end{aligned} \]

Rearranging and setting MR(Q) = MC(Q) \[ \frac{(𝑃^∗−𝑀C^∗)}{𝑃^∗} =\frac{1}{ |\epsilon_{𝑄,𝑃}| } \]

Inverse elasticity pricing rule (IEPR): The less price elastic the demand, the higher the optimal markup

Demand Elasticity

Market B is less price elastic than A, thus the markup is higher in B than in A

Market Power

  • When a firm can exercise some degree of control over its price in the market, we say that it has market power

  • Monopolists or producers of differentiated products will, in general, charge prices that exceed their marginal cost

  • A natural measure of market power is \((P − MC)/P\)

    • Lerner Index
  • The Lerner Index is zero for a perfectly competitive industry. It is positive for any industry that departs from perfect competition.

Market Power

  • The IEPR tells us that in the equilibrium of a monopoly market, the Lerner Index will be inversely related to the market price elasticity of demand.

  • An important driver of the price elasticity of demand is the threat of substitute products outside the industry

  • If a monopoly market faces strong competition from substitute products, the Lerner Index can still be low. In other words, a firm might have a monopoly, but its market power might still be weak.

Why Monopolies Exist?

  • Read Ch. 11.6

  • Natural Monopolies

    • Economies of scale
    • Demand
  • Barriers to entry

    • Structural
    • Legal
    • Strategic

Monopsony

  • A monopsony market consists of a single buyer facing many sellers

  • The monopsonist’s profit maximization problem:

    • \(\max \pi = TR – TC = Pf(L) – w(L)L\)
    • where: \(Pf(L)\) is the total revenue for the monopsonist
    • and \(w(L)L\) is the total cost
  • The monopsonist’s profit maximization condition:

    • \(MRP_L = ME_L\)
    • \(P \times MP_L = dTC/dL\)
    • \(P (dQ/dL) = w + L (dw/dL)\)

Inverse Elasticity Pricing Rule

  • Monopsony equilibrium condition results in:
    • \((MRP_L−w)/w=1/\epsilon_{L,w}\)
    • where: \(\epsilon_{L,w}\) is the price elasticity of labor supply, \((w/L)(dL/dw)\)

Monopsony DWL

  • Consumer (Monopsony firm) gets A+B+C

  • Producer (Workers) gets D

  • The deadweight loss is F+G

Problems

Comparative Statics

  • Shifts in demand

    • Shifting intercept up or down
  • Shifts in MC

  • Constant MC and linear demand (Monopoly Midpoint Pricing Rule)

Monopolies with Multiple Plants

  • Two markets
  • Cartel

Taxes and Monopolies

Monoposony and the Minimum Wage